There are often recipes I find online that I am interested in trying, but the ingredients are all in cups rather than grams. How do you convert them? I once tried, and and it ended in disastrous results.

Cups are measured in volume rather than weight, so there is no simple conversion that applies for all ingredients. For things like flour, one cup is about the equivalent of 250g. If you know that, and have a basic idea of baking ratios, then you should be able to work out how many grams you need of other staple ingredients like butter.

When it comes to items that have a larger volume, but a much lighter weight - such as spinach leaves - it becomes trickier. What would be really useful if if we could use this question article as a kind of database. People could write down the conversion for certain ingredients, and readers could refer to it when looking at the recipes on this site.

Unfortunately you can't make the conversion simply, as it depends entirely on the density of what you are measuring.

Water is well known for having 1ml=1g. Oil on the other hand, is much less dense than water, and so 1ml weighs less than a gram.
Some common conversions are:
1 cup of water: 250g
1 cup plain flour: 128g
1 cup white sugar: 201g

It's worth using a converter like this one as the density of each and every ingredient is different.

If your recipe is very finicky I highly recommend using weight and not volume because the volume will change with temperature. Again, water is a great example of this: think of how water increases in volume when frozen, yet its weight remains the same. Using weight for measurements is especially important in soap making and other chemical reactions.

I was really shocked when I learned that most people supposedly don't own a set of kitchen scales (especially in the US apparently). There's a much larger margin of error when you're measuring via. cups because there are so many things that affect it.

For instance, a cup of flour from the US will often weigh less than a cup of cake flour from Australia. It's something to do with fine the flour is and how much its been sifted.

I believe it really just comes down to experimenting. Always weigh your ingredients, even when they're in cups, and when you have a combination that works perfectly, adjust your recipe to suit measurements.

I don't think you can. A cup is a measurement where grams are weights. Different foods and different have different densities so you would have to get some scales for your grams but measuring cups for cup measurements. Measuring spoons come in handy too.